Solving a Three-Force Member Equilibrium of Particles Question

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The discussion focuses on solving a three-force member equilibrium problem in mechanics. The participant has created a free body diagram (FBD) and identified the forces involved but is unsure how to proceed using three-force member theory. Another contributor suggests breaking down the known and unknown forces into their x and y components and applying the three equilibrium equations to find the unknowns. The original poster acknowledges familiarity with equilibrium equations but struggles specifically with the three-force member approach. The conversation highlights the complexity of applying this theory and references additional resources for guidance.
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Homework Statement



2055-1262.jpg


Homework Equations


None


The Attempt at a Solution


The prof told us to treat the three-force member as an equilibrium of particle question. So here is the FBD and the triangle I set up for the particle equilibrium:
2055-126.jpg


I don't know where to go from there.. I mean I know it's a right angle triangle, where I know the hypotenuse, but that's really it. Help? :)
 
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Your first FBD is good. It is usually best to break up the known (3kN) and unknown (A and B) forces into their x and y components. Then just use the 3 equilibrium equations (sum of x forces =0, sum of y forces = 0, and sum of moments about any point = 0) which will give you the required 3 equatiions to solve for the 3 unknowns A, B, and alpha.
 
Thanks Jay. I know how to do it with the equilibrium equations actually. But I'm having problems doing it using the three-force member theory...
 
Melawrghk said:
Thanks Jay. I know how to do it with the equilibrium equations actually. But I'm having problems doing it using the three-force member theory...

That's a pain theory to use, but if it is required by the problem, the steps are shown here at
http://darkwing.uoregon.edu/~struct/courseware/461/461_lectures/461_lecture15/461_lecture15.html
I've never used the graphical method.
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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